Question : Richard can finish a work in 13 days. Joseph can finish the same work in 14 days while Thomas can finish the work in 15 days. How long will it take to finish it if they work together?
Correct Answer 4 382/587 days or 4.651 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Richard = 13 days
And, the number of days required to finish the same work by Joseph = 14 days
And, the number of days required to finish the same work by Thomas = 15 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 13 days the work is done by Richard = 1
∴ The work done by Richard in 1 day = 1/13
Similarly,
∵ In 14 days the work is done by Joseph = 1
∴ The work done by Joseph in 1 day = 1/14
Similarly,
∵ In 15 days the work is done by Thomas = 1
∴ The work done by Thomas in 1 day = 1/15 part
Now, the work done by Richard, Joseph, and Thomas together in 1 day
= Richard's 1 day work + Joseph's 1 day work + Thomas's 1 day work
= 1/13 + 1/14 + 1/15
= 210 + 195 + 182/2730
= 587/2730 part of work
This means in 1 day, 587/2730 part of work is done by Richard, Joseph and Thomas working together.
Now, the number of days required to finish 587/2730 part of work by Richard, Joseph, and Thomas working together = 1
∴ the number of days required to finish the whole work (1 work) by Richard + Joseph + Thomas together
= 1/587/2730
= 1 × 2730/587 = 2730/587 days
= 4 382/587 days = or 4.651 days
Thus, Richard, Joseph, and Thomas working together will finish the total work (1 work) in 4 382/587 days = or 4.651 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Richard = 13 days
And the number of days required to finish the same work by Joseph = 14 days
And the number of days required to finish the work by Thomas = 15 days
Thus, the number of days required to finish the work by Richard, Joseph, and Thomas together = ?
Here a = 13 days
And, b = 14 days
And, c = 15 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Richard, Joseph, and Thomas working together
= 13 × 14 × 15/13 × 14 + 13 × 15 + 14 × 15 days
= 2730/182 + 195 + 210 days
= 2730/587 days
= 2730/587 days
= 4 382/587 days or 4.651
Thus, Richard, Joseph, and Thomas together will finish the work in 4 382/587 days or 4.651 days Answer
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